The half-filled Landau level: The case for Dirac composite fermions

Area of Science:

• Condensed matter physics
• Quantum Hall effect
• Topological phases of matter

Background:

• Correlations in two-dimensional electron gases (2DEGs) under strong magnetic fields create emergent excitations.
• Composite fermions, theorized as electron-flux composites, are predicted to form a Fermi sea experiencing zero net magnetic field.

Purpose of the Study:

• To numerically verify the existence of the composite fermion Fermi sea.
• To investigate the properties and symmetries of this exotic state.
• To explore the relevance of Dirac particle phenomenology in this context.

Main Methods:

• Infinite-cylinder density matrix renormalization group (DMRG) numerical simulations were employed.
• Analysis focused on identifying emergent excitations and their characteristics.

Main Results:

• The existence of the composite fermion Fermi sea was numerically verified.
• The phase was found to exhibit particle-hole symmetry.
• Suppression of 2k(F) backscattering, characteristic of Dirac particles, was observed.

Conclusions:

• Composite fermions in this regime behave as massless Dirac particles, analogous to topological insulator surface states.
• The findings highlight the relevance of Dirac fermion phenomenology to 2DEGs in the quantum Hall regime.
• Particle-hole symmetry is crucial for the self-consistency of this composite fermion state.